Sony Xperia z2 edges still big(the upper and lower)
The edges are still big(the upper and lower).There are smartphones with the same size or smaller and they have 5.5 inch display.
If you are comparing with LG G3, than there is a lot of differences in both phone. For one, the power and volume buttons for G3 is located behind the phone, not easily accessible. G3 is not dust and water resistance like S5 or Z2. G3 is wider and thicker than Z2. G3 camera app cannot choose manual settings compare to Z2.
So if G3 is what you are looking for, you can still sell your Z2, top up the difference and buy G3.